The algorithm used is in close agreement with that published by Fan, Panaye, Doucet, and Barbu in 1993. (J. Chem. Inf. Comput. Sci. 1993, 33, 657-662)
The functions contained in rings determines the smallest set of smallest rings (SSSR) from a molecule graph.
The aromaticity of the rings is tested using the 4n+2 pi electron rule of Huckel.
Graph Theory
The algorithm relies on some knowledge of graph theory.
- A RING can be represented as R(n1,n2,...) where ni are the atomic indices.
- The first selected NODE is called the ROOT.
- A PATH walked that starts and ends at the ROOT NODE is called CLOSED.
- CONNECTIVITY of a node is defined as the number of links to other nodes.
- A NODE with a single link to another NODE is called TERMINAL.
- A BLOCK is a group of NODES such that all links between them are involved in one or more rings
The SSSR of a molecule is represented as S(m1,m2,...) where mi are the ring sizes.
An OPEN ACYCLIC NODE is an acyclic atom which is not located between two blocks.
A CLOSED ACYCLIC NODE is an acyclic atom located between two blocks.
Graphical Illustration of the SSSR Algorithm
- Take for example the following molecule:
- Highlighting all OPEN ACYCLIC NODES
- Remove all OPEN ACYCLIC NODES
- Highlighting all CLOSED ACYCLIC NODES
- Remove all CLOSED ACYCLIC NODES
- How many rings are there in the current block?
- Let NODE 1 be the ROOT NODE, we can produce numerous ring systems including R(1,2,3,15,13,14), R(1,2,3,15,16,10,11,12,13,14), etc. How do we know we have found the smallest ring? The closed path found containing the ROOT NODE is recursively searched until it can not be reduced further, in other words R(1,2,3,15,13,14) is found.
- Once an irreducible closed path is found all NODES with two links are removed. NODES 2, 1, and 14 can safely be removed. The algorithm then picks another ROOT NODES and the next ring is found until all are found.
Huckel Rule of Aromaticity
The algorithm used is in close agreement with that published by Roos-Kozel, and Jorgensen in 1981. (J. Chem. Inf. Comput. Sci. 1981, 21, 101-111)
- Rings are classified as aromatic (AR), antiaromatic (AA), or nonaromatic (NA). A ring system is aromatic if and only if it contains 4n+2 (n=0,1,2,3,4,...) pi electrons and is planar.
- Nonaromatic are screened using the following rules:
- No intra-ring double bonds
- contains quaternary atom
- contains more than one saturated carbon
- contains a monoradical
- contains a sulfoxide or sulfone
- The number of electrons atom contribute in simple aromatics (no exocyclic pi bonds):
- 0 = cationic carbon and boron
- 2 = saturated heteroatoms
- 2 = anionic carbon
- 1 = radicals not on pi bond
- 1 = atoms on intra-ring pi bond
- Rings thats contain exocyclic pi bonds are
Ring Centroid
![\[ XYZ^{c} = {1 \over N} \sum_{i}^{N}XYZ_{i} \]](form_115.png)
Ring Normal and Plane
- Form the coordinate matrix of the ring atoms
![\[ XYZ^{ring} = XYZ^{ring} - XYZ^{c} \]](form_116.png)
- Principal Component Analysis of the Ring Coordinate Correlation Matrix
![\[ C = X^{T}X \]](form_117.png)
![\[ CP = \lambda_{i}P \]](form_118.png)
![\[ P = P + XYZ^{c} \]](form_119.png)
- The first two eigenvectors define the plane of the ring, while the third defines the ring normal.
